Claudia Sheinbaum has secured a historic victory to become Mexico's first female president, inheriting the legacy of her mentor and outgoing leader Andres Manuel Lopez Obrador. Sheinbaum, a climate scientist and former mayor of Mexico City, clinched the presidency with an impressive 58.3% to 60.7% of the vote, according to a rapid sample count by Mexico's electoral authority. This marks the highest percentage in Mexico's democratic history.

The ruling coalition, of which Sheinbaum is a part, is poised to attain a possible two-thirds super majority in both houses of Congress. This majority would enable them to pass constitutional reforms without needing support from opposition parties, according to preliminary results.

Her opponent, Xochitl Galvez, garnered between 26.6% and 28.6% of the vote and has conceded defeat. "For the first time in the 200 years of the republic, I will become the first woman president of Mexico," Sheinbaum declared to jubilant supporters.

Sheinbaum's victory is a significant milestone in a country known for its traditional values and gender roles. "I never imagined that one day I would vote for a woman," said 87-year-old Edelmira Montiel, a Sheinbaum supporter in Tlaxcala. "Thank God that has changed and I get to live it," she added.

The new president faces a complex road ahead, promising to increase popular welfare policies amidst a heavy budget deficit and low economic growth. Sheinbaum emphasized her commitment to fiscal responsibility and respect for the autonomy of the central bank.

Improving security is another key challenge. The election, the most violent in Mexico's modern history with 38 candidates murdered, underscores the grave security issues. Organized crime groups have expanded their influence during Lopez Obrador's term.

Addressing these security challenges will be crucial for Sheinbaum. "Unless she commits to making a game-changing level of investment in improving policing and reducing impunity, Sheinbaum will likely struggle to achieve a significant improvement in overall levels of security," said Nathaniel Parish Flannery, an independent Latin America political risk analyst.

On the international front, Sheinbaum will need to navigate negotiations with the United States over U.S.-bound migrant flows and security cooperation in the fight against drug trafficking. The outcome of U.S. elections could potentially complicate these negotiations.

Domestically, the new president will need to tackle electricity and water shortages, attract manufacturers under the nearshoring trend, and address the challenges of Pemex, the state oil giant facing declining production and significant debt.

"She cannot just rely on endless public money without making the company profitable," noted Alberto Ramos, chief Latin America economist at Goldman Sachs, regarding Pemex.

Lopez Obrador's policies, including a doubled minimum wage and reduced poverty rates, have been popular successes. Sheinbaum aims to expand welfare programs, though she faces the hurdle of a looming deficit and sluggish GDP growth.

In her victory speech, Sheinbaum expressed gratitude to Lopez Obrador, acknowledging his transformative impact on the country. Despite opposition claims, she rejected assertions that she would be a mere "puppet" of her mentor, pledging to continue policies that have benefited Mexico's poorest citizens.